Combinatorial Optimization Algorithms for Dynamic Multiple Fault Diagnosis in Automotive and Aerospace Applications

In this thesis, we develop dynamic multiple fault diagnosis (DMFD) algorithms to diagnose faults that are sporadic and coupled. Firstly, we formulate a coupled factorial hidden Markov model-based (CFHMM) framework to diagnose dependent faults occurring over time (dynamic case). Here, we implement a mixed memory Markov coupling model to determine the most likely sequence of (dependent) fault states, the one that best explains the observed test outcomes over time. An iterative Gauss-Seidel coordinate ascent optimization method is proposed for solving the problem. A soft Viterbi algorithm is also implemented within the framework for decoding dependent fault states over time. We demonstrate the algorithm on simulated and real-world systems with coupled faults; the results show that this approach improves the correct isolation rate as compared to the formulation where independent fault states are assumed.;Secondly, we formulate a generalization of set-covering, termed dynamic set-covering (DSC), which involves a series of coupled set-covering problems over time. The objective of the DSC problem is to infer the most probable time sequence of a parsimonious set of failure sources that explains the observed test outcomes over time. The DSC problem is NP-hard and intractable due to the fault-test dependency matrix that couples the failed tests and faults via the constraint matrix, and the temporal dependence of failure sources over time. Here, the DSC problem is motivated from the viewpoint of a dynamic multiple fault diagnosis problem, but it has wide applications in operations research, for e.g., facility location problem. Thus, we also formulated the DSC problem in the context of a dynamically evolving facility location problem. Here, a facility can be opened, closed, or can be temporarily unavailable at any time for a given requirement of demand points. These activities are associated with costs or penalties, viz., phase-in or phase-out for the opening or closing of a facility, respectively.;The set-covering matrix encapsulates the relationship among the rows (tests or demand points) and columns (faults or locations) of the system at each time. By relaxing the coupling constraints using Lagrange multipliers, the DSC problem can be decoupled into independent subproblems, one for each column. Each subproblem is solved using the Viterbi decoding algorithm, and a primal feasible solution is constructed by modifying the Viterbi solutions via a heuristic. The proposed Viterbi-Lagrangian relaxation algorithm (VLRA) provides a measure of suboptimality via an approximate duality gap. As a major practical extension of the above problem, we also consider the problem of diagnosing faults with delayed test outcomes, termed delay-dynamic set-covering (DDSC), and experiment with real-world problems that exhibit masking faults. Also, we present simulation results on OR-library datasets (set-covering formulations are predominantly validated on these matrices in the literature), posed as facility location problems.;Finally, we implement these algorithms to solve problems in aerospace and automotive applications. Firstly, we address the diagnostic ambiguity problem in aerospace and automotive applications by developing a dynamic fusion framework that includes dynamic multiple fault diagnosis algorithms. This improves the correct fault isolation rate, while minimizing the false alarm rates, by considering multiple faults instead of the traditional data-driven techniques based on single fault (class)-single epoch (static) assumption. The dynamic fusion problem is formulated as a maximum a posteriori decision problem of inferring the fault sequence based on uncertain outcomes of multiple binary classifiers over time. The fusion process involves three steps: the first step transforms the multi-class problem into dichotomies using error correcting output codes (ECOC), thereby solving the concomitant binary classification problems; the second step fuses the outcomes of multiple binary classifiers over time using a sliding window or block dynamic fusion method that exploits temporal data correlations over time. We solve this NP-hard optimization problem via a Lagrangian relaxation (variational) technique. The third step optimizes the classifier parameters, viz., probabilities of detection and false alarm, using a genetic algorithm. The proposed algorithm is demonstrated by computing the diagnostic performance metrics on a twin-spool commercial jet engine, an automotive engine, and UCI datasets (problems with high classification error are specifically chosen for experimentation). We show that the primal-dual optimization framework performed consistently better than any traditional fusion technique, even when it is forced to give a single fault decision across a range of classification problems.;Secondly, we implement the inference algorithms to diagnose faults in vehicle systems that are controlled by a network of electronic control units (ECUs). The faults, originating from various interactions and especially between hardware and software, are particularly challenging to address. Our basic strategy is to divide the fault universe of such cyber-physical systems in a hierarchical manner, and monitor the critical variables/signals that have impact at different levels of interactions. The proposed diagnostic strategy is validated on an electrical power generation and storage system (EPGS) controlled by two ECUs in an environment with CANoe/MATLAB co-simulation. Eleven faults are injected with the failures originating in actuator hardware, sensor, controller hardware and software components. Diagnostic matrix is established to represent the relationship between the faults and the test outcomes (also known as fault signatures) via simulations. The results show that the proposed diagnostic strategy is effective in addressing the interaction-caused faults.